Answer by Rory Young:
Every animal has a "fight or flight" zone. For example if you approach a rat from a distance it will run away but corner it in a hole and put your finger in there and it will bite you!
Elephants are the same, get too close and they could either give you a "mock charge" (i.e. intimidation zone) or a "full charge" (attack zone). How close this distance is depends on the elephant and the situation.
Females tend to be more aggressive Females with young will be even more aggressive than females without young and the most aggressive of all are tusk-less females. Tusk-less females are most likely so easily upset because of a feeling of insecurity acquired from not having tusks to defend themselves and therefore compensate for this perceived or real weakness by becoming more aggressive.
Males, although generally more laid back, turn into complete lunatics when in "musth". Here is a quote from Wikipedia on musth:
"Musth or must (pron.:) is a periodic condition in bull (male) , characterized by highly aggressive behavior and accompanied by a large rise in reproductive hormones – levels in an elephant in musth can be as much as 60 times greater than in the same elephant at other times."
Basically it is linked to rut and one could write a whole book on the subject. They become completely mad and will go out of their way to charge and attack anyone and anything, including other males, other animals, trees, bushes, people, cars and have even killed their keepers and trainers. Here is a newspaper report about the death of a keeper in Livingstone in Zambia. I knew the man who died:
Here is a picture of a bull in musth chasing a giraffe:
I have personally come across bulls in musth on many occasions and usually get the hell out of their way as soon as I see the usual combination of seeping temporal gland, wet and extended penis and aggressive posture and gait. On one occasion when in a vehicle I had such a bull go out of his way for over half a kilometer after hearing the vehicle (he wouldn't have been able to see it at that distance) and then chase me for some distance. Once I had accelerated out of range he plowed his tusks into the ground in a display of frustration and anger> The only thing that seems to calm them down is a female in season and such females will often attach themselves to a bull in musth to avoid being harassed by lots of males.
Bulls can also be dangerous even when not in musth. Here is a report, also from Livingstone in Zambia about a man killed by two elephants (both males as indicated by the fact that there were only two and therefore also not in musth as bulls in musth are always on their own or around a herd of females).
So, in a nutshell; yes unprovoked elephants can and do attack and kill humans.